scholarly journals Triglobal infinite-wing shock-buffet study

2021 ◽  
Vol 925 ◽  
Author(s):  
Wei He ◽  
Sebastian Timme
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Base Flow ◽  
Sweep Angle ◽  
Aspect Ratios ◽  
Spatially Periodic ◽  
Time Marching ◽  
High Reynolds ◽  
Limiting Case ◽  
Base Flows

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

1996 ◽  
Vol 326 ◽  
pp. 399-415 ◽  
Author(s):  
M. Wanschura ◽  
H. C. Kuhlmann ◽  
H. J. Rath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Onset Of Convection ◽  
Buoyant Convection ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Prandtl Numbers

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

scholarly journals Stability analysis of the elliptic cylinder wake

2014 ◽  
Vol 763 ◽  
pp. 302-321 ◽  
Author(s):  
Justin S. Leontini ◽  
David Lo Jacono ◽  
Mark C. Thompson
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Cylinder Wake ◽  
Long Wavelength ◽  
Aspect Ratios ◽  
Numerical Stability Analysis ◽  
Spatiotemporal Symmetries ◽  
Three Dimensional Simulations

AbstractThis paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

2015 ◽  
Vol 768 ◽  
pp. 113-140 ◽  
Author(s):  
Vincenzo Citro ◽  
Flavio Giannetti ◽  
Luca Brandt ◽  
Paolo Luchini
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Closed Orbit ◽  
Three Dimensional ◽  
Base Flow ◽  
Open Cavity ◽  
Critical Conditions ◽  
Global Mode ◽  
Structural Sensitivity

The viscous and inviscid linear stability of the incompressible flow past a square open cavity is studied numerically. The analysis shows that the flow first undergoes a steady three-dimensional bifurcation at a critical Reynolds number of 1370. The critical mode is localized inside the cavity and has a flat roll structure with a spanwise wavelength of about 0.47 cavity depths. The adjoint global mode reveals that the instability is most efficiently triggered in the thin region close to the upstream tip of the cavity. The structural sensitivity analysis identifies the wavemaker as the region located inside the cavity and spatially concentrated around a closed orbit. As the flow outside the cavity plays no role in the generation mechanisms leading to the bifurcation, we confirm that an appropriate parameter to describe the critical conditions in open cavity flows is the Reynolds number based on the average velocity between the two upper edges. Stabilization is achieved by a decrease of the total momentum inside the shear layer that drives the core vortex within the cavity. The mechanism of instability is then studied by means of a short-wavelength approximation considering pressureless inviscid modes. The closed streamline related to the maximum inviscid growth rate is found to be the same as that around which the global wavemaker is concentrated. The structural sensitivity field based on direct and adjoint eigenmodes, computed at a Reynolds number far higher than that of the base flow, can predict the critical orbit on which the main instabilities inside the cavity arise. Further, we show that the sub-leading unstable time-dependent modes emerging at supercritical conditions are characterized by a period that is a multiple of the revolution time of Lagrangian particles along the orbit of maximum growth rate. The eigenfrequencies of these modes, computed by global stability analysis, are in very good agreement with the asymptotic results.

The stability of the variable-density Kelvin–Helmholtz billow

2008 ◽  
Vol 612 ◽  
pp. 237-260 ◽  
Author(s):  
JÉRÔME FONTANE ◽  
LAURENT JOLY
Keyword(s):  
Stability Analysis ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Variable Density ◽  
Base Flow ◽  
Shear Instability ◽  
Numerical Continuation ◽  
Small Scale ◽  
Two Dimensional ◽  
Two Fluids

We perform a three-dimensional stability analysis of the Kelvin–Helmholtz (KH) billow, developing in a shear layer between two fluids with different density. We begin with two-dimensional simulations of the temporally evolving mixing layer, yielding the unsteady base flow fields. The Reynolds number is 1500 while the Schmidt and Froude numbers are infinite. Then exponentially unstable modes are extracted from a linear stability analysis performed at the saturation of the primary mode kinetic energy. The spectrum of the least stable modes exhibits two main classes. The first class comprises three-dimensional core-centred and braid-centred modes already present in the homogeneous case. The baroclinic vorticity concentration in the braid lying on the light side of the KH billow turns the flow into a sharp vorticity ridge holding high shear levels. The hyperbolic modes benefit from the enhanced level of shear in the braid whereas elliptic modes remain quite insensitive to the modifications of the base flow. In the second class, we found typical two-dimensional modes resulting from a shear instability of the curved vorticity-enhanced braid. For a density contrast of 0.5, the wavelength of the two-dimensional instability is about ten times shorter than that of the primary wave. Its amplification rate competes well against those of the hyperbolic three-dimensional modes. The vorticity-enhanced braid thus becomes the preferred location for the development of secondary instabilities. This stands as the key feature of the transition of the variable-density mixing layer. We carry out a fully resolved numerical continuation of the nonlinear development of the two-dimensional braid-mode. Secondary roll-ups due to a small-scale Kelvin–Helmholtz mechanism are promoted by the underlying strain field and develop rapidly in the compression part of the braid. Originally analysed by Reinoud et al. (Phys. Fluids, vol. 12, 2000, p. 2489) from two-dimensional non-viscous numerical simulations, this instability is shown to substantially increase the mixing.

Symmetry breaking and instability mechanisms in medium depth torsionally driven open cylinder flows

2011 ◽  
Vol 672 ◽  
pp. 521-544 ◽  
Author(s):  
STUART J. COGAN ◽  
KRIS RYAN ◽  
GREGORY J. SHEARD
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Symmetry Breaking ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Interfacial Region ◽  
Nonlinear Stability Analysis ◽  
Aspect Ratios ◽  
Instability Modes

A numerical investigation was conducted into the different flow states, and bifurcations leading to changes of state, found in open cylinders of medium to moderate depth driven by a constant rotation of the vessel base. A combination of linear stability analysis, for cylinders of numerous height-to-radius aspect ratios (H/R), and nonlinear stability analysis and three-dimensional simulations for a cylinder of aspect ratio 1.5, has been employed. Attention is focused on the breaking of SO(2) symmetry. A comprehensive map of transition Reynolds numbers as a function of aspect ratio is presented by combining a detailed stability analysis with the limited existing data from the literature. For all aspect ratios considered, the primary instabilities are identified as symmetry-breaking Hopf bifurcations, occurring at Reynolds numbers well below those of the previously reported axisymmetric Hopf transitions. It is revealed that instability modes with azimuthal wavenumbers m = 1, 3 and 4 are the most unstable in the range 1.0 < H/R < 4, and that numerous double Hopf bifurcation points exist. Critical Reynolds numbers generally increase with cylinder aspect ratio, though a decrease in stability occurs between aspect ratios 1.5 and 2.0, where a local minimum in critical Reynolds number occurs. For H/R = 1.5, a detailed characterisation of instability modes is given. It is hypothesized that the primary instability leading to transition from steady axisymmetric flow to unsteady three-dimensional flow is related to deformation of shear layers that are present in the flow, in particular at the interfacial region between the vortex breakdown bubble and the primary recirculation.

Channel formation by turbidity currents: Navier–Stokes-based linear stability analysis

2008 ◽  
Vol 615 ◽  
pp. 185-210 ◽  
Author(s):  
B. HALL ◽  
E. MEIBURG ◽  
B. KNELLER
Keyword(s):  
Shear Stress ◽  
Stability Analysis ◽  
Linear Stability ◽  
Suspended Sediment Concentration ◽  
Three Dimensional ◽  
Sediment Concentration ◽  
Base Flow ◽  
Navier Stokes ◽  
Streamwise Vortices ◽  
Sediment Bed

The linear stability of an erodible sediment bed beneath a turbidity current is analysed, in order to identify potential mechanisms responsible for the formation of longitudinal gullies and channels. On the basis of the three-dimensional Navier–Stokes equations, the stability analysis accounts for the coupled interaction of the three-dimensional fluid and particle motion inside the current with the erodible bed below it. For instability to occur, the suspended sediment concentration of the base flow needs to decay away from the sediment bed more slowly than does the shear stress inside the current. Under such conditions, an upward protrusion of the sediment bed will find itself in an environment where erosion decays more quickly than sedimentation, and so it will keep increasing. Conversely, a local valley in the sediment bed will see erosion increase more strongly than sedimentation, which again will amplify the initial perturbation.The destabilizing effect of the base flow is modulated by the stabilizing perturbation of the suspended sediment concentration and by the shear stress due to a secondary flow structure in the form of counter-rotating streamwise vortices. These streamwise vortices are stabilizing for small Reynolds and Péclet numbers and destabilizing for large values.For a representative current height of O(10–100m), the linear stability analysis provides the most amplified wavelength in the range of 250–2500m, which is consistent with field observations reported in the literature. In contrast to previous analyses based on depth-averaged equations, the instability mechanism identified here does not require any assumptions about sub- or supercritical flow, nor does it require the presence of a slope or a slope break.

scholarly journals Hydrodynamic behavior of a bare rod bunle

1977 ◽  
Author(s):  
Ιωάννης Μπαρτζής
Keyword(s):  
Secondary Flow ◽  
Turbulent Flows ◽  
Axial Velocity ◽  
Nuclear Reactor ◽  
Three Dimensional ◽  
Hydrodynamic Behavior ◽  
Rod Bundle ◽  
Aspect Ratios ◽  
Strong Candidate ◽  
High Reynolds

Temperature distributions within the rod bundle of a nuclear reactor is of major importance in nuclear reactor design. However temperature information presupposes knowledge of the hydrodynamic behavior of the coolant which is the most difficult part of the problem due to complexity of the turbulence phenomena. In the present work a 2-equation turbulence model - a strong candidate for analyzing actual three dimensional turbulent flows - has been used to predict fully developed flow of infinite bare rod bundle of various aspect ratios (P/D). The model has been modified to take into account anisotropic effects of eddy viscosity. Secondary flow calculations have been also performed although the mo^el seems to be too rough to predict the secondary flow correctly. Heat Transfer calculations have been performed to confirm the importance of anisotropic viscosity in temperature predictions. All numerical calculations for flow and heat have been performed by two computer codes developed in the present work which were based on the TEACH code [71]· Also experimental measurements of the distribution of axial velocity, turbulent axial velocity, turbulent kinetic energy and radial Reynoldsstresses were performed in the developing and fully developed regions. A 2-channel Laser Doppler Anemometer working on the Reference mode with forward scattering was used to perform the measurements in a simulated interior subchannel of a triangular rod array with P/D=1.124. Comparisons between the analytical results and the results of this experiment as well as other experimental data in rod bundle array available in literature are presented. The predictions are in good agreement with the results for the high Reynolds numbers.

Linear instability analysis of convection in a laterally heated cylinder

2014 ◽  
Vol 747 ◽  
pp. 447-459 ◽  
Author(s):  
Bo-Fu Wang ◽  
Zhen-Hua Wan ◽  
Zhi-Wei Guo ◽  
Dong-Jun Ma ◽  
De-Jun Sun
Keyword(s):  
Prandtl Number ◽  
Hydrodynamic Instability ◽  
Critical Rayleigh Number ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Central Zone ◽  
Linear Instability ◽  
Base Flow ◽  
Aspect Ratios

AbstractThe three-dimensional instabilities of axisymmetric flow are investigated in a laterally heated vertical cylinder by linear stability analysis. Heating is confined to a central zone on the sidewall of the cylinder, while other parts of the sidewall are insulated and both ends of the cylinder are cooled. The length of the heated zone equals the radius of the cylinder. For three different aspect ratios, $A= 1.92 $, 2, 2.1 ($A=\mathrm{height}$/radius), the dependence of the critical Rayleigh number on the Prandtl number (from 0.02 to 6.7) has been studied in detail. For such a kind of laterally heated convection, some interesting stability results are obtained. A monotonous instability curve is obtained for $A= 1.92 $, while the instability curves for $A= 2 $ and $A= 2.1 $ are non-monotonous and multivalued. In particular, an instability island has been found for $A=2$. Moreover, mechanisms corresponding to different instability results are obtained when the Prandtl number changes. At small Prandtl number, the flow is oscillatory unstable, which is dominated by hydrodynamic instability. At intermediate Prandtl number, the interaction between buoyancy and shear in the base flow plays a more important role than pure hydrodynamic instability. At even higher Prandtl number, Rayleigh–Bénard instability becomes the dominant process and the flow loses stability through steady bifurcation.

Transient growth in developing plane and Hagen Poiseuille flow

2005 ◽  
Vol 461 (2057) ◽  
pp. 1311-1333 ◽  
Author(s):  
Peter W Duck
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Alternative Mechanism ◽  
Fully Developed Flow ◽  
Circular Pipes ◽  
Flow Disturbances ◽  
High Reynolds ◽  
The Stability

The stability of developing entry flow in both two-dimensional channels and circular pipes is investigated for large Reynolds numbers. The basic flow is generated by uniform flow entering a channel/pipe, which then provokes the growth of boundary layers on the walls, until (far downstream) fully developed flow is attained; the length for this development is well known to be (Reynolds number)×the channel/pipe width/diameter. This enables the use of high-Reynolds-number theory, leading to boundary-layer-type equations which govern the flow; as such, there is no need to impose heuristic parallel-flow approximations. The resulting base flow is shown to be susceptible to significant, three-dimensional, transient (initially algebraic) growth in the streamwise direction, and, consequently, large amplifications to flow disturbances are possible (followed by ultimate decay far downstream). It is suggested that this initial amplification of disturbances is a possible and alternative mechanism for flow transition.

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